Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

some sort of skeletal code is present in the grooves, and that the
various record players add their own interpretations to that code?
Tortoise: I don't know, for sure. The cagey Crab wouldn't fill me in on all
the details. But I did get to hear a third song, when record player B-I0
swiveled into place.
Achilles: How did it go?
Tortoise: The melody consisted of enormously wide intervals, and went
B-C-A-H.

, ~.

J

~ ~r

I

I

The interval pattern in semitones was;

-10, +33, -10.

It can be gotten from the CAGE pattern by yet another multiplication

by 3 %, and rounding to whole numbers.

Achilles: Is there a name for this kind of interval multiplication?

Tortoise: One could call it "intervallic augmentation". It is similar to the

canonic device of temporal augmentation, where all the time values of

notes in a melody get multiplied by some constant. There, the effect is

just to slow the melody down. Here, the effect is to expand the melodic

range in a curious way.

Achilles: Amazing. So all three melodies you tried were intervallic aug-

mentations of one single underlying groove-pattern in the record?

Tortoise: That's what I conclyded.

Achilles: I find it curious that when you augment BACH you get CAGE,

and when you augment CAGE over again, you get BACH back, except

jumbled up inside, as if BACH had an upset stomach after passing

through the intermediate stage of CAGE.

Tortoise: That sounds like an insightful commentary on the new art form

of Cage.

Canon by Intervallic Augmentation^157